In rhombus BEAM, find ∠AME and ∠AEM.
Solution:
Given, BEAM is a rhombus.
We have to find ∠AME and ∠AEM.
Given, ∠BAM = 70°
We know that the diagonals of a rhombus bisect at 90 degrees.
So, ∠AOM = 90°
Considering triangle AOM ,
By angle sum property of a triangle,
∠AOM + ∠AMO + ∠MOA = 180°
90° + ∠AMO + 70° = 180°
160° + ∠AMO = 180°
∠AMO = 180° − 160°
∠AMO = 20°
We know that all the sides are equal in a rhombus.
So, BE = EA = AM = MB
In triangle AME,
EA = AM
We know that the angles opposite to the equal sides are equal.
∠AME = ∠AEM = 20°
Therefore, the values of ∠AEM and ∠AME are 20° and 20°.
✦ Try This: In parallelogram BEAM, find ∠AME and ∠AEM.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 148
In rhombus BEAM, find ∠AME and ∠AEM.
Summary:
In rhombus BEAM, the values of ∠AEM and ∠AME are 20° and 20°.
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